标题： 光线空间：因果性和$L$-边界 显示英文标题

标题： The space of light rays: Causality and $L$-boundary

摘要： 光射线空间$\mathcal{N}$的共形洛伦兹流形$(M,\mathcal{C})$在一些拓扑条件下是一个流形，其基本元素是未参数化的零测地线。这个流形$\mathcal{N}$受 R. 彭罗斯的扭量理论强烈启发，保留了$M$的所有信息，可以作为补充时空模型的空间。在本综述中，$\mathcal{N}$的几何及相关结构，如天空空间$\Sigma$和接触结构$\mathcal{H}$被介绍。 $M$的因果结构被描述为$\mathcal{N}$几何的一部分。 由 R. Low 提出的时空$M$的新因果边界，即$L$边界，在$3$维流形$M$的情况下被构造，并被提出作为一般维数构造的模型。 它的定义仅依赖于$\mathcal{N}$的几何结构，而与时空$M$的几何结构无关。 由$L$边界$\partial M$所满足的性质可以用来描述所得到的扩展$\overline{M}=M\cup \partial M$，并且这种描述也适用于一般维度。 显示英文摘要

摘要： The space of light rays $\mathcal{N}$ of a conformal Lorentz manifold $(M,\mathcal{C})$ is, under some topological conditions, a manifold whose basic elements are unparametrized null geodesics. This manifold $\mathcal{N}$, strongly inspired on R. Penrose's twistor theory, keeps all information of $M$ and it could be used as a space complementing the spacetime model. In the present review, the geometry and related structures of $\mathcal{N}$, such as the space of skies $\Sigma$ and the contact structure $\mathcal{H}$, are introduced. The causal structure of $M$ is characterized as part of the geometry of $\mathcal{N}$. A new causal boundary for spacetimes $M$ prompted by R. Low, the $L$-boundary, is constructed in the case of $3$-dimensional manifolds $M$ and proposed as a model of its construction for general dimension. Its definition only depends on the geometry of $\mathcal{N}$ and not on the geometry of the spacetime $M$. The properties satisfied by the $L$-boundary $\partial M$ permit to characterize the obtained extension $\overline{M}=M\cup \partial M$ and this characterization is also proposed for general dimension.